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For easier handling, reorder the terms of the polynomial $7x^2+x^3+14x+8$ from highest to lowest degree
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$\int\frac{x+3}{x^3+7x^2+14x+8}dx$
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((x+3)/(7x^2+x^314x+8))dx. For easier handling, reorder the terms of the polynomial 7x^2+x^3+14x+8 from highest to lowest degree. We can factor the polynomial x^3+7x^2+14x+8 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals 8. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^3+7x^2+14x+8 will then be.